Projective planes and congestion-free networks

Projective planes and congestion-free networks

| The design of networks using broadcast media so that every two sites lie on a common link, subject to constraints on the number of links at each site (degree), and the number of sites on each link (link size), is examined. A method proposed by Yener, Ofek, and Yung is shown to fail in general to achieve the minimum link size for a speciied degree constraint. The existence of (k; n)-arcs in pr...

Affine and projective planes

Smooth Projective Planes

Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to CP. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plane curves are smooth collineations, and prove a variety of results analogous to the theory ...

Projective Planes in Algebraically

We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particul...

Extending Partial Projective Planes

If a finite partial projective plane can be extended to a projective plane of order n, then it can be extended by a sequence of one line extensions. We describe necessary conditions for such an extension to exist, and restrictions which can be imposed on the intermediate sequence of extensions. This method can be used to attempt to construct a projective plane of non-prime-power order. 1. Parti...